Robust controller design for multivariable nonlinear uncertain systems

A QFT-type frequency-domain controller design technique is presented for multiple input-multiple ouput (MIMO) nonlinear systems with significant structured (parametric) uncertainty. Hard time-domain constraints are imposed on the outputs and control inputs in response to step disturbances. The control design method is based on replacing the nonlinear MIMO system with an equivalent diagonal MIMO linear uncertain plant using compact and convex sets of output functions. Then, a diagonal controller is designed for the equivalent linear system by transferring the time-domain constraints into the frequency-domain to obtain a series of allowable regions for the frequency responses of the nominal loop transfer functions. Next, a loop-shaping procedure is used to shape the nominal loop transfer function and hence the controller for each loop. Finally, Schauder’s fixed point theorem is utilized to show that the same controller will also work for the nonlinear system. The proposed method is illustrated by an example.